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Reorganizationofnurseschedulingreducestheriskofhealthcareassociatedinfections

EugenioValdano1,ChiaraPoletto2,Pierre-YvesBoëlle2,VittoriaColizza2

1CenterforBiomedicalModeling,TheSemelInstituteforNeuroscienceandHumanBehavior,DavidGeffenSchoolofMedicine,760WestwoodPlaza,UniversityofCaliforniaLosAngeles,LosAngeles,CA90024,USA

2INSERM,SorbonneUniversité,InstitutPierreLouisd’EpidémiologieetdeSantéPublique(IPLESP),75012,Paris,France

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ABSTRACT

Background.Efficientpreventionandcontrolofhealthcareassociatedinfections(HAIs)isstillanopenproblem.

Objective.Todesignefficienthospitalinfectioncontrolstrategiesbyreorganizingnursescheduling.

Design,setting,andparticipants.Proof-of-conceptmodelingstudybasedonhigh-resolutioncontactdatafromwearablesensorsbetweenpatients,nurses,doctors,andadministrativestaffatashort-staygeriatricwardofaUniversityhospital.

Methods.WeconsideredisolationandcontactremovaltoidentifythemostimportantclassofindividualsforHAIdissemination.Weintroducedanovelinterventionbasedonthereorganizationofnursescheduling.Thisstrategyswitchesandreassignsnurses’tasksthroughtheoptimizationofshifttimelines,whilerespectingfeasibilityconstraintsandsatisfyingpatient-carerequirements.WeevaluatedtheimpactofinterventionsthroughaSusceptible-Colonized-Susceptibletransmissionmodelontheempiricalandreorganizedcontacts.

Results.Isolationandcontactremovalproducedthelargestriskreductionwhenactingonnurses.ReorganizingtheirschedulesreducedHAIriskby27%(95%confidenceinterval[24,29]%)whilepreservingthetimeliness,number,anddurationofcontacts.Morethan30%nurse-nursecontactsshouldbeavoidedtoachieveanequivalentreductionthroughsimplecontactremoval.Nooverallchangeinthenumberofnursesperpatientresultedfromtheintervention.

Conclusions.ReorganizationofnurseschedulingoffersanalternativechangeofpracticethatsubstantiallylimitsHAIriskinthewardwhileensuringthetimelinessandqualityofhealthcareservices.Thiscallsforincludingoptimizationofnurseschedulingpracticesinprogramsforbetterinfectioncontrolinhospitals.

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Healthcareassociatedinfections(HAIs)areincreasinglywidespread,withanestimated4millionindividualsaffectedeachyearinEurope,representingapproximately6%ofallhospitalizedpatients(1).Theseinfectionshaveasubstantialimpactonmorbidityandassociatedcostsforthehealthcaresystem,potentiallyleadingtofailureoftreatment,longerillnessesandhospitalizations,anddeaths.Risingantimicrobialresistanceinhospitalshasalsoincreasedthethreattohumanhealth,asresistantpathogensmaycauseseriousinfectionsthatcannotbetreatedwithavailabledrugs(2).

CommonHAIsspreadthroughclose-rangeproximityorphysicalcontactsbetweenindividuals.SeveralstudieshighlightedtheimportanceofcontactsforHAIdiffusion(3–9),showinghowlargervarietyanddurationofcontactsareassociatedtoanincreaseinHAIrisk(10,11).Thesefactorsleadtothewell-knownparadoxthathealthcareworkersplayakeyroleinpathogendisseminationbecauseoftheirfrequentandpersistentcontactswithindividualsofdifferentcategories(12).BeingathigherriskforHAIcolonization,healthcareworkersmayactastransientsuperspreadersandtransmittheinfectiontothelargenumberofindividualstheygetincontactwith,especiallyinthevulnerablepopulationofpatients(12–14).

Infectioncontrolstrategiestargetinghealthcareworkersrequirecarefuldesign,toavoidinterferingwiththeirabilitytocarryouttheircorehealthcareresponsibilities.HygienicmeasuressuchashandsanitizingaretheprimarystrategytopreventHAIdiffusion,aimingtoreducetheper-contactriskoftransmission(15).Theefficacyofthesemeasuresishoweverlimitedbylowcompliancerates,asreportedbyseveralstudiesespeciallyunderconditionsofemergencyorunderstaffing(12,16–18).EvenlowcompliancebyafewindividualscanhaveadisproportionateimpactontheriskofHAIdiffusioninthehospital,giventhepresenceofpotentialsuperspreaders(11,12,19,20).Otherapproachesforinfectioncontrolhavethereforeconsideredtheuseofpersonalprotectiveequipment(e.g.facemasksandgloves)(21),vaccination(22),isolation,ornursecohorting(i.e.assigningnursestoalimitednumberofpatientsduringagivenworkingperiod)(23).Theireffectiveness,however,isstillmatterofdebate(23,24).Mostimportantly,someofthesemeasuresmayonlybeapplicableinreactiontooutbreaks,astheyarerathercostlyanddisruptive.Itmaythusprovedifficulttointegratethemintoday-to-dayhospitalactivities.

Routineoperationsinahospitalareensuredbyadequatehealthcareworkersstaffingandscheduling.Theirorganizationhasbeenextensivelystudiedforseveraldecadesinoperationsresearch,management,andcomputerscience(25,26)andisgenerallyknownasthe‘nurseschedulingproblem’.Ittypicallyinvolvestheoptimizationofsingleormultiplegoalswhilesatisfyingasetofhardconstraints–i.e.featuresthatneedtoberespectedatallcosts,e.g.feasibility,workload,lengthofshifts,requiredpersonnelorskills–andasetofsoftconstraints–i.e.aspectsthataredesirablebutmaynotbemetinordertoachieveasolution,e.g.preferencesforadayoff.Mathematicallydescribedbytheconstrainedminimizationofapotentialfunction,thesolutiontotheschedulingproblemaimstooptimizehumanresources’efficiency,patientsafety,qualityofmedicalservices,costs,andstaffsatisfaction.Despitethegreatinterestinthetopic,researchhassofaraddresseditexclusivelyfromthemanagementandcomputationalperspectives(25,26),withnoregardstoitspotentialroleininfectioncontrol.

Hereweproposeaproof-of-conceptmodelingstudyforhospitalinfectioncontrolbasedonthereorganizationofcareinahospitalwardthroughchangesinthescheduleofworkshiftsofnurses.Usinghigh-resolutiontemporalrecordsoncontactsinahospitalward(3),ourapproachswitchestasksbetweennursesbyalteringtheirworkschedulesthroughtheoptimizationofa

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potentialfunction,similarlytomodelsfornursescheduling.Thereorganizedschedulemaintainsfullstaffcapacityatanygiventime,preservesalltime-referencedcontactsrecordedinthedatasetwithoutaffectingqualitystandardsofmedicalservices,andrespectsbasicoccupationalconstraints(weeklyworkload,lengthofaworkshift).Thestudyisappliedtoashort-staygeriatrichospitalwardinLyon,France,wherecontactdatawerecollectedthroughautomatedsensors(3).Wemodelthecirculationdynamicsofhand-transmittedpathogenssuchasmethicillin-resistantStaphylococcusaureus(MRSA)orvancomycin-resistantEnterococci(VRE)intheward,andevaluatetheeffectivenessoftheinterventionbymeasuringtheriskforHAIdiffusion.

METHODS

Contactdata

Weusedpubliclyavailableanonymizeddatacollectedduring4daysand4nights(December6to10,2010)atashort-staygeriatricwardofahospitalinLyon,France(3,27).UsingwearableRFIDsensors,thesystemtrackedface-to-faceproximitycontactsovertimebetween75participatingindividuals,including27nurses(N),11doctors(D),8administrativestaff(A),and29patients(P).ThedatasetwasfirstanalyzedinRef.(3);Figure1reportsitsbasicproperties.Nursesanddoctorshadthelargestcumulativedurationofcontacts,andmostfrequentcontactswereobservedbetweennurses(NN),andbetweenpatientsandnurses(PN).

HAIriskestimate

Thetime-resolvedcontactsarerepresentedintheformofatemporalcontactnetwork(28),wherenodescorrespondtoindividualsandlinkstoproximityencounters.Timeevolutionoccursatanhourlytimescale.WemodelHAIdiffusioninthehospitalwardthroughaSusceptible–Colonized–Susceptibletransmissiondynamicsonthetemporalcontactnetwork(6,8,19,29,30).Colonizedindividualstransmitthepathogenwithprobability𝜆percontact.Theiraveragecolonizationdurationisfixedat10hoursforhealthcareworkers,assumingaspontaneouslyclearingtransientcolonizationattheendofaworkshift.Thedurationislongerforpatientsandcorrespondsto10days,hypothesizingaweeklybacterialscreening,followedby3daystoobtaintestresultsandimplementadecolonizationtherapy,asin(6,19).

Toassesstheriskoftransmissionoftheinfectionintheward,weestimatetheconditionforcirculationofMRSAorVREonmeasuredcontactsthroughtheinfectionpropagatorapproach(31–33).Thistheoreticalframeworkwasintroducedtostudyepidemicsspreadingontemporalnetworksandidentifythecriticalvalue𝜆" ofthetransmissibilityabovewhichthepathogenspreadsinthehostpopulation(i.e.if𝜆 > 𝜆" anoutbreakispredictedtooccur).TheAppendixreportsafulldescriptionofthisapproach,andtheavailablesoftwaretool.

Interventionthroughisolationorcontactremoval

ToassesstherolethateachclassofindividualshasonHAIrisk,wesimulatetwointerventionsbased(i)ontheisolationofindividualsbelongingtoagivenclass,and(ii)ontheremovalofcontactsestablishedbetweentwoclasses(e.g.contactsbetweenpatientsandnurses).Eachinterventionismadecomparableacrossclassesorpairsofclasses,throughtheisolationof8individuals(i.e.thesmallestsizeclass)ortheremovalof5%ofthetotaldurationofcontactsinthedataset,respectively.Interventionsarerepeatedtoaccountforthestochasticityinthechoiceofthenodetoisolateorofthecontactstoremove.

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Interventionbasedonreorganizationofnursescheduling

Weintroduceanactivityvariable𝑎%(𝑡)associatedtonurse𝑖duringhour𝑡,sothat𝑎%(𝑡)=1ifthenurseisatworkandestablishescontactsinthathourand𝑎%(𝑡) = 0otherwise(Figure2a).Foreachnurse,wecomputetheshiftduration𝑠definedasthenumberofconsecutiveworkhours,andtheworkload𝑤correspondingtothetotalnumberofhoursworkedinthedataset.

Theproposedinterventionswitchesandreassignsthetasksperformedbytwonursesinagivenhour𝑡.Tasksconsistincontactsthatnursesestablish,astheyperformtheirdutiesininteractionwithotherindividuals(e.g.caringforapatient).Theycorrespondtopossibletransmissionevents.Thereorganizationisdrivenbytheminimizationofthefollowingpotentialfunction:

𝑉 = −01∑ ∑ ∑ 𝑎%(𝑡3)𝑎%(𝑡1)(𝑡3 − 𝑡1)14546% .(2)

𝑖runsonallnurses,𝑡3and𝑡1runonthewholetimeline,and𝑘determinesthetendencyofthepotential(𝑘 = ±1).𝑘 = −1showsatendencytocreateregularindividualschedules(periodicactivitypatterns),and𝑘 = 1atendencyforirregularindividualschedules(erraticactivitypatterns)(Fig.2b).

Thisstrategypreservesthenumber,type,andexacttimelineofcontacts,differentlyfromtheinterventionthroughcontactremovals.Theminimizationofthepotentialisadditionallysubjecttofeasibilityconstraintsonshiftdurationandworkloadofnurses:

• Model𝑆:theexchangeisallowedaslongaseachworkingshiftlastsatmosts=10hours,asmeasuredempirically.

• Model𝑊𝑆:inadditiontotheconstraintonshiftduration,theexchangeisallowedonlyifitpreservestheempiricallymeasuredworkloadwofeachnurse.

Eachmodelisrunwithbothvaluesof𝑘,foratotalof4reorganizationoptions(𝑆=3, 𝑆?3,𝑊𝑆=3,𝑊𝑆?3).TheAppendixreportsadetaileddescriptionoftheminimizationalgorithms.Despitebeingsynthetic,theseinterventionshaveanincreasingdegreeofrealismtoshowthepotentialofthisproof-of-conceptstudyforpossibleapplicationsinrealsituations.

Evaluationofinterventions

WeevaluatetheeffectofinterventionsbycomparingtheresultingHAIriskestimate(𝜆"@AB)withtheoneestimatedontheempiricalpatternofcontacts(𝜆"CDE).WedefinetheHAIriskreductionastherelativevariationofthesetwoquantities((𝜆"@AB − 𝜆"CDE)/𝜆"CDE),sothatapositiveriskreductioncorrespondstointerventionsimprovingthecontrolofpotentialHAIdiffusioninthehospitalward(theoppositefornegativevalues).FluctuationsintheHAIriskreductionareobtainedfromthevariationsresultingfromthestochastictrials.

Effectsofthereorganizationofnurseschedulingoncontactpatterns

Totestwhethertheproposedreorganizationofnurseschedulingleadstonursecohorting(23),wemeasurethevariationinthenumberofdistinctnursesassignedtoeachpatientfollowingtheinterventioncomparedtotheempiricalvalue.Negativevaluesofthisvariationcorrespondtonursecohorting(i.e.anaveragereductionofthenumberofnursesperpatient).

Wealsomeasurethevariationsinthenurses’degree(i.e.numberofdistinctconnectionseachnurseestablishes)bycomparingaveragedegreeandassociatedfluctuationsbeforeandafterthereorganization.

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RESULTS

Interventionthroughisolationorcontactremoval

Completeisolationof8randomlychosenpatientscorrespondstoadropof8%inthecumulateddurationofcontacts,whileisolating8nursesreducesitby31%(Figure3a).Inthelattersituation,itleadstoanapproximate35%medianreductionoftheHAIrisk(Fig.3c),whereasthesameinterventionappliedtootherclasseshasnegligibleimpact.

Whenremovingacertainfractionofcontactsbetweenclasses,thelargestriskreductionisobtainedbyactingonnurse-nursecontacts(medianreductionof13%),correspondingtodeleting15%ofnurse-nursecontactduration(Fig.3b,d).Interventionsoncontactsbetweennursesanddoctorsoradministrativestaff,whichareproportionallymoredisruptive,havealmostnoimpactontherisk.

Boththeoreticalinterventionshighlightthecentralroleplayedbynursesinthehospitalwardunderstudy,supportingthedesignofamorerealisticinterventionthatcouldactonnurseactivitieswithoutdisruptingthewardfunctioningandtheprovisionofmedicalandnursingservices.

Interventionbasedonreorganizationofnursescheduling

Minimizingthepotentialwhileconstrainingonlythemaximumshiftdurationleadstotwodifferentprofilesoftheworkloaddistribution(Figure4).Model𝑆=3showsapproximatelyhalfofthenursesnotworking(𝑤 = 0),andtherestdistributedquiteevenlyfromshorttoverylongworkloads(Fig.4a).Model𝑆?3tendsinsteadtohomogenizenurses’workloadaroundtheaveragevalue(16to23hoursinthe4-daytimeframe,Fig.4c).

Shiftdurationdistributionsarerathersimilarinallmodels,andqualitativelycomparablewithempiricaldata(Fig.4b,d,f,h).Smallvariationson1-hourshifts(higherprobabilityin𝑊𝑆models)and8-9-hourshifts(moremarkedincreaseinthe𝑆models)areobserved.

Model𝑆?3achievesthelargestreductionofHAIrisk(median27%reduction,95%CI[24,29]%),followedby𝑊𝑆=3(21%,[20,24]%)and𝑊𝑆?3(19%,[16,20]%)(Figure5a).Equivalentriskreductionswouldbeobtainedbycontactremovalifmorethan30%,25%,and20%durationofnurse-nursecontactsweretoberemoved,respectively(Fig.5b).Model𝑆=3insteadincreasesHAIriskof5%.

Models𝑆?3 ,𝑊𝑆=3,and𝑊𝑆?3,whichdecreaserisk,showareductionofthefluctuationsinthenumberofdistinctcontactsestablishedbynurses,withoutsubstantiallyalteringtheiraveragenumberofcontactsorthenumberofdistinctnursesassignedtoeachpatient(Figure6).Model𝑆=3 ,whichincreasesrisk,raisescohortinglevelswithamedianof4lessnursesassignedtoeachpatientandstronglyincreasesnurses’degreefluctuations.

DISCUSSION

Thekeyroleofhealthcareworkersinthetransmissionofhealthcareassociatedinfectionsiswidelyrecognized(12–15).Lowcomplianceandlimitedsustainabilityofrecommendedstrategieshinderefficientinfectioncontrol.OurstudyproposesanalternativechangeofpracticethroughthereorganizationofnurseworkshiftstoreduceHAIrisk.Usingsensedcontactdatainahospitalward,weshowthatreassigningtaskstonursesminimizingapotentialfunctionon

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theirtimelineofactivitycanreducetheriskofHAIdiffusionbyaboutonethird.Ourfindingsshowthepotentialofplanningnurseschedulestoimproveinfectionpreventionandcontrol.

Thekeyadvantageoftheproposedinterventionisthatitpreservesthenumber,type,anddurationofcontactsateachtime.Thisensuresthetimelinessandqualityofmedicalandnursingservicesprovided.Anequivalentimpactonriskreductioncouldbeachievedbylimitingtheinteractionsviablefortransmission.Uninformedremovalofcontactswouldbehoweverratherdisruptive,withonethirdofcontactsdeletedamongnurses,attheexpenseofstandardsofcare.Patientisolation,staffcohorting,andincreaseinstafflevelswereshowninpreviousworktobeeffectiveinlimitingtransmission,bydirectlyorindirectlyactingontheinteractions(18,23,29).Fullyisolatingabout30%ofpatientsintheward,however,hadnoimpactontheriskoftransmissioninthisstudy.Also,thehighestimprovementininfectioncontrol(𝑆?3)wasdueneithertocohortingnortoanincreaseinstafflevels.However,thisinterventionledtothestrongestreductioninthefluctuationsinthenumberofdistinctcontactspernurse.Homogenizingnurses’contactpatternsaround40-45contactspernurseremovesthepresenceofpotentialsuperspreaders(11,12,19,20)thatcouldotherwiseactasriskamplifiers.ThereductioninthedegreefluctuationsisindeedobservedonlyinthemodelsreducingHAIrisk.

Adequatestaffinglevelsandreasonableworkloadsareestablishedfactorspromotinginfectionpreventioninhospitals(12,18,34).Reorganizingnurses’shiftsjustrespectingthemaximumshiftdurationconstraint(model𝑆=3)resultsinourstudyinapproximatelyhalfofthestaffnotworking,whilenursingcareisassignedtotheremaininghalf,thusforcingunrealisticworkschedules(upto80hoursofworkpernursein4days,i.e.anaverageof20h/day).Suchreorganizationofworkhasanegativeimpactoninfectioncontrol,inlinewithempiricalfindingsthatrecognizehighworkloads,understaffing,andthepresenceofsuperspreadersaskeyriskfactorsforMRSAcirculationinhealthcaresettings(12,34).Inaddition,poorinfectioncontrolwouldbehereassociatedtoanincreaseofcohortinglevels,whichsimplyresultsfromlowerstaffing.AllothermodelsleadinsteadtoanimportantreductionofHAIrisk,withthereorganizationbeingabletobreakpotentialchainsoftransmissionthroughtheswappingoftasks.Improvedcontrolisachievedbyreducingthepresenceofsuperspreadersintheward,underbothregularandirregularindividualworktimelinesofnurses,andwithdifferentshiftandworkloaddistributions.Thesefindingsuncoverthepracticalmechanismforimprovedcontrolandhighlightstherobustnessoftheproposedstrategytodifferentrequirementsontheorganizationoftheworkforce.

Mathematicalmodelshavealreadybeenusedtoimproveourunderstandingofhospitalepidemiology(35,36).Theyarenowadaysincreasinglydata-driventhankstoremotesensing,allowinganautomatedcollectionofclose-proximityinteractionsbetweenindividuals,notaffectedbyreportingorobserverbiasesinherenttootherapproaches(37).ThistypeofcontactswasrecentlyshowntoexplainthediffusionpathofseveralHAIs(6,7,10,38).Forthisreason,ourfindingsextendtopathogensotherthanMRSAandVRE,spreadingalongthesameroutes,underthehypothesisofrelativelyrapiddecolonization(6,19).Durationsoftheorderofmonthsthatareempiricallyobservedinabsenceofinterventions(39)werenotexaminedherebecauseconsideredinappropriateinthehypothesisofdecontaminationtakingplace.

PriormodelingworkgenerallyreliedonnumericalsimulationsofHAIspread(35).WeusedtheinfectionpropagatorapproachtoestimateHAIriskreductioninareliableandcomputationallyfastway.Thisapproachwasalreadyusedtoestimatetheriskofdiseasepersistenceinotherepidemiccontexts(32,33),andhastheadvantageofbeingflexibletotheintegrationof

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heterogeneitiesintheforceofinfectionthatmaydepend,forexample,onclass-specifictransmissibility.

Theproposedreorganizationofstaffschedulesfocusedontheclassofnurses,astheoreticalresultsonisolationorcontactremovalclearlyidentifiednursesasthecategoryofhealthcareworkerswhomostlycontributetothetransmissionriskintheward.Thiscanbetracedbacktothelargernumberandlongerdurationofcontactsestablishedbynurses,commonlyrequiredbynursingcare,anditisinlinewithpreviousobservationsandmodelingworksproposingnursesastargetgroupforpreventionmeasures(7,9,22).

Ourfindingsshowthepotentialtointegrateinfectionpreventionintothenurseschedulingproblem,originallydesignedtooptimizehospitalworkforce.However,somestepsarestillneededtocarrythisnovelparadigmintopractice,intheformofaroadmaptoafuturehospitalprotocol.First,contactdatacollectiononalongertimeframeisrequiredtoprovideacomprehensivemeasurementofthefunctioningofthehealthcaresettingunderstudy.Moreover,collectingmetadataonthetypeofclinicalinterventionsperformedintheward,thespecificrolesofsubclassesofpersonnel(e.g.nursetypes),thetypeofpatientsadmitted,andthestandardandorganizationofcare(e.g.schedulingpracticesalongthe24hours)iskeytoimprovetheparameterizationoftheepidemictransmissionmodelanddefinetheconditionsfortask’reassignments(e.g.byswappingsimilartasks,ortasksthatcanbehandledbythesamestafftype).Mostimportantly,suchadditionaldatawillhelpconstrainthepotentialfunctiontopatientneedsandstaffrequirements.Welist,forexample,thelengthofshifts,thenumberofweekendsworked,thenumberofon/offdays,theroleofadditionalpersonnel(e.g.physicaltherapists,nutritionists,withdifferentworkingpatterns),theuseofpart-timeandtemporarynursingpersonnel(thusintroducingstaffforsubstituteshifts).Integratingtheseelementswouldmakethere-schedulingfeasible,withoutalteringthecoreofthestrategyproposedhere.

Wepresentedmodelingevidencethatreorganizingnurseschedulingwhilemaintainingthenumber,timeliness,andqualityofmedicalservicesprovidedbynursingstaffcanstronglydecreasetheriskforHAIdiffusioninthehospitalward.Ourstudyprovidesthetheoreticalbasisforanewcontrolparadigm,showingitspotentialforintegrationinfuturenurseschedulingpracticesfortheimplementationofsuccessfulinfectioncontrolprogramsatthehospitals.

ACKNOWLEDGEMENTS

Financialsupport.ThisstudywaspartiallysupportedbytheFrenchANRprojectSPHINX(ANR-17-CE36-0008-05)toVC.

Potentialconflictofinterest.Allauthorsreportnoconflictsofinterestrelevanttothisarticle.

Thankyounotes.WeacknowledgetheScientificEvolutionaryWritingworkshop(www.sew-workshop.org)wherepartofthispaperwaswritten.

ETHICSSTATEMENT

ThecontactdatausedinthisstudywerecollectedinaresearchapprovedbytheFrenchnationalbodiesresponsibleforethicsandprivacy,the“CommissionNationaledel’Informatiqueetdes

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Libertés”(CNIL,http://www.cnil.fr)andthe“ComitédeProtectiondespersonnes”(http://www.cppsudest2.com/)ofthehospital.

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19. TemimeL,OpatowskiL,PannetY,Brun-BuissonC,BoëllePY,GuillemotD.Peripatetichealth-careworkersaspotentialsuperspreaders.ProcNatlAcadSci.2009Oct27;106(43):18420–5.20. Lloyd-SmithJO,SchreiberSJ,KoppPE,GetzWM.Superspreadingandtheeffectofindividualvariationondiseaseemergence.Nature.2005Nov;438(7066):355.21. RobergeRJ.Faceshieldsforinfectioncontrol:Areview.JOccupEnvironHyg.2016;13(4):235–42.22. PolgreenPM,TassierTL,PemmarajuSV,SegreAM.Prioritizinghealthcareworkervaccinationsonthebasisofsocialnetworkanalysis.InfectControlHospEpidemiol.2010Sep;31(9):893–900.23. CooperBS,StoneSP,KibblerCC,CooksonBD,RobertsJA,MedleyGF,etal.IsolationmeasuresinthehospitalmanagementofmethicillinresistantStaphylococcusaureus(MRSA):systematicreviewoftheliterature.BMJ.2004Sep2;329(7465):533.24. McLawsM-L.Therelationshipbetweenhandhygieneandhealthcare-associatedinfection:it’scomplicated.InfectDrugResist.2015;8:7–18.25. SiferdSP,BentonWC.Workforcestaffingandscheduling:Hospitalnursingspecificmodels.EurJOperRes.1992Aug10;60(3):233–46.26. BurkeEK,DeCausmaeckerP,BergheGV,VanLandeghemH.TheStateoftheArtofNurseRostering.JSched.2004Nov1;7(6):441–99.27. SocioPatterns.org[Internet].[cited2018Aug28].Availablefrom:http://www.sociopatterns.org/28. HolmeP,SaramäkiJ.TemporalNetworks.PhysRep.2012Oct;519(3):97–125.29. UenoT,MasudaN.Controllingnosocomialinfectionbasedonstructureofhospitalsocialnetworks.JTheorBiol.2008Oct7;254(3):655–66.30. StehléJ,VoirinN,BarratA,CattutoC,ColizzaV,IsellaL,etal.SimulationofanSEIRinfectiousdiseasemodelonthedynamiccontactnetworkofconferenceattendees.BMCMed.2011;9:87.31. ValdanoE,FerreriL,PolettoC,ColizzaV.AnalyticalComputationoftheEpidemicThresholdonTemporalNetworks.PhysRevX.2015Apr8;5(2):021005.32. ValdanoE,PolettoC,ColizzaV.Infectionpropagatorapproachtocomputeepidemicthresholdsontemporalnetworks:impactofimmunityandoflimitedtemporalresolution.EurPhysJB[Internet].2015Dec[cited2016Jan3];88(12).Availablefrom:http://link.springer.com/10.1140/epjb/e2015-60620-533. DarbonA,ColombiD,ValdanoE,SaviniL,GiovanniniA,ColizzaV.Diseasepersistenceontemporalcontactnetworksaccountingforheterogeneousinfectiousperiods.RSocOpenSci.2019Jan;6(1):181404.34. ViccaAF.Nursingstaffworkloadasadeterminantofmethicillin-resistantStaphylococcusaureusspreadinanadultintensivetherapyunit.JHospInfect.1999Oct;43(2):109–13.35. BontenMJ,AustinDJ,LipsitchM.Understandingthespreadofantibioticresistantpathogensinhospitals:mathematicalmodelsastoolsforcontrol.ClinInfectDisOffPublInfectDisSocAm.2001Nov15;33(10):1739–46.36. AssabR,NekkabN,CrépeyP,AstagneauP,GuillemotD,OpatowskiL,etal.Mathematicalmodelsofinfectiontransmissioninhealthcaresettings:recentadvancesfromtheuseofnetworkstructureddata.CurrOpinInfectDis.2017Aug;30(4):410–8.37. MastrandreaR,FournetJ,BarratA.ContactPatternsinaHighSchool:AComparisonbetweenDataCollectedUsingWearableSensors,ContactDiariesandFriendshipSurveys.PLOSONE.2015Sep1;10(9):e0136497.38. DuvalA,ObadiaT,BoëlleP-Y,FleuryE,HerrmannJ-L,GuillemotD,etal.CloseproximityinteractionssupporttransmissionofESBL-K.pneumoniaebutnotESBL-E.coliinhealthcaresettings.PLOSComputBiol.2019May30;15(5):e1006496.39. MarschallJ,MühlemannK.Durationofmethicillin-resistantStaphylococcusaureuscarriage,accordingtoriskfactorsforacquisition.InfectControlHospEpidemiol.2006Nov;27(11):1206–12.

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FIGURES

Figure1:Contactsinthehospitalward.Percentageofparticipatingindividuals(a),ofcontacts(b),andofcontactduration(c)byclassofindividuals(patients(P),nurses(N),doctors(D),administrativepersonnel(A)).(d):Percentageofcontactdurationbetweenclassesof

individuals.(e):Hourlytimelineofthenumberofindividualsperclassestablishingcontacts.

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Figure2:Interventiononnursescheduling.(a)Schematicvisualizationoftheintervention,withtheexchangeoftasksbetweennurse𝑖(filledbluenode)andnurse𝑗(voidbluenode),attimes𝑡(whiletheyarebothatwork)and𝑡 + 1(whilenurse𝑗isnotatworkintheempiricalschedule,andwouldexchangehershiftwithnurse𝑖inthereorganizedschedule).Links

representcontactswithotherindividuals(blacknodes).Thereorganizednurseschedule(right)iscomparedtotheempiricalone(left)obtainedfromthecontactdata.(b)Exampleofan

empiricalnurseschedulealongwiththere-organizedonesobtainedwith𝑘 = −1and𝑘 = −1,leadingtoregularandirregularindividualschedules,respectively.Greyblockscorrespondto

hourswhenthenurseisatwork.

Nurse i

Nurse j

ai (t) =1 ai (t+1) =1

aj (t) =1 aj (t+1) =0

ai (t) =1 ai (t+1) =0

aj (t) =1 aj (t+1) =1

REORGANIZEDEMPIRICAL(a)

(b)

EMPIRICAL

REG (-1)

IRREG (+1)

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Figure3:Impactofinterventionthroughisolationorcontactremovals.(a):Medianpercentageofcontactdurationremovedwithintheclass(redline)orofthefulltimeline(greybars)once8individualsineachclassareisolated,correspondingto28%ofpatients(P),30%ofnurses(N),73%ofdoctors(D),and100%ofadministrativestaff(A).(b):Medianpercentageofcontactdurationremovedamonglinksestablishedbynurseswithotherclasses(greybars,withpatients(PN),withnurses(NN),withdoctors(ND),withadministrativestaff(NA)),once5%ofthetotalcontactdurationofthefulltimelineisremoved(redline).(c),(d):HAIriskreductionin

thehospitalwardachievedthroughisolation(panelc)orcontactremoval(paneld)correspondingtotheresultsofpanelsaandb,respectively.Boxplotsindicatethemedian,interquartilerangeand95%CIoftheriskreduction,accountingforthestochasticityofthe

interventions(resultsfrom20randomtrials).

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Figure4:Workloadandshiftdurationinthereorganizedschedule.(a)-(b):Probabilitydistributionofnurses’workload𝑤(panela)andshiftduration𝑠(panelb)followingthe

reorganizationofshifts,comparedtotheempiricaldistributions.Thereorganizationisbasedonmodel𝑆=3(i.e.constraintonshiftdurationandattractivepotential).(c)-(d),(e)-(f),(g)-(h):Aspanels(b)and(c)formodel𝑆?3(constraintonshiftdurationwithrepulsivepotential),model𝑊𝑆=3(constraintonworkloadandshiftdurationwithattractivepotential),model𝑊𝑆?3

(constraintonworkloadandshiftdurationwithrepulsivepotential),respectively.

(a) (b)

(c) (d)

(e) (f)

(g) (h)

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Figure5:Impactofinterventionthroughreorganizationofnursescheduling.(a):HAIriskreductioninthehospitalwardachievedwiththereorganizationofnurseschedulinginthe

models𝑆=3, 𝑆?3,𝑊𝑆=3,𝑊𝑆?3,comparedtotheempiricalsituation.Boxplotsindicatethemedian,interquartilerangeand95%CIoftheriskreduction,accountingforthestochasticityofthe

exchange(resultsfrom50randomtrials).(b):Percentageofcontactdurationtoberemovedinthenurse-nurseinteractionssothattheinterventionthroughcontactremovalwouldachievethesameriskreductionsofpanela(obtainedthroughthereorganizationofnursescheduling).𝑆=3

isnotshownasithasanegativeimpactontherisk.

(a)

(b)

(%)

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Figure6:Effectofreorganizationoncontactpatterns.(a)Variationofthenumberofdistinctnursesassignedtoeachpatient,inthereorganizedvs.empiricalcontactpattern.(b)Average

numberofdistinctcontactspernurse(nurses’degree).Dashedlinecorrespondstotheempiricalvalue.(c)Fluctuations(standarddeviation)ofthenumberofdistinctcontactspernurse.Dashedlinecorrespondstotheempiricalvalue.For(a),(b),(c),resultsareobtainedfrom500random

trials.

(a)

(b)

(c)

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APPENDIX

1.InfectionpropagatorapproachtoevaluatetheHAIrisk

Werepresentthetime-evolutionofcontactsintermsofatemporalnetworkwithadjacencymatrices𝐴4 ,with𝑡runningonthe1-hourtimesteps.Theentry𝑖, 𝑗of𝐴4 isequaltooneifnodes𝑖, 𝑗establishacontactduringtimestep𝑡,zerootherwise.WemodelthespreadofthepathogenusingaSusceptible–Colonized–Susceptiblemodel.Acolonizednodeinthenetworktransmitsthepathogentoaconnectednodewithprobability𝜆(transmissibility)ateachtimestep.Italsoclearsthepathogenwithaprobability𝜇ateachtimestep.𝜇=3isthentheaveragecarriageperiod.Thereexistsacriticalvalueoftransmissibility𝜆"–calledepidemicthreshold–thatdeterminestheglobalbehavioroftheoutbreak.Iftransmissibilityishigherthantheepidemicthreshold(𝜆 > 𝜆"),introducingthepathogenintothehospitalwardislikelytocausealarge-scaleoutbreak.Instead,iftransmissibilityislowerthantheepidemicthreshold(𝜆 < 𝜆"),theoutbreakislikelytoaffectfewindividuals.Therefore,computingchangesintheepidemicthresholdisaasyntheticandeasy-to-interpretwaytoweightheimpactofanypolicy,onthevulnerabilityofthewardtothepathogenconsidered.Iftheepidemicthresholdincreasesfollowingintervention,thewardbecomesmoreresilienttopathogenintroduction.Oppositely,iftheepidemicthresholdgoesdown,thewardbecomesmorepronetolarge-scaleoutbreaks.ThisistherationalebehindourdefinitionofHAIriskreduction:(𝜆"@AB − 𝜆"CDE)/𝜆"CDE .Inordertocomputeit,weneedtocomputetheepidemicthresholdbeforeandafterintervention.Tothatend,weemploytheinfectionpropagatorapproach(31–33),whichcancomputetheepidemicthresholdonanyarbitrarytemporalnetwork,forthespreadingmodelusedhere.Theinfectionpropagatoristhefollowingmatrix:

𝑃(𝜆, 𝜇) = ∏ (1 − 𝜇 + 𝜆𝐴4)4 .

Itcontainsboththetime-evolvingstructureofthecontactnetwork(𝐴4),andtheparametersofthespreadingmodel(𝜆, 𝜇),andmeasuresthechainsofinfectionbetweenindividualsalongwhichthepathogencanspread.Weprovein(31–33)thattheepidemicthresholdisthesmallestvalueof𝜆forwhichthelargesteigenvalueof𝑃equalsone.

WeprovideaPythonlibrarytocomputetheepidemicthresholdofanyempiricaltemporalnetworkinthefollowingrepository:https://github.com/eugenio-valdano/threshold

2.Implementationofswitchandreassignmentofnurses’tasksandminimizationofthepotential

WeminimizethepotentialusingtheMetropolisalgorithm.Itisaniterativeprocessbasedonthefollowingsteps.

Versionfor𝑆?3, 𝑆=3:

1) Choosetwonurses(𝑖 ≠ 𝑗),andonetimestep(𝑡);2) Ifneithernurseisactiveduring𝑡,goto1);3) Swaptasksbetween𝑖, 𝑗during𝑡;4) Iftheswapbreaksthe𝑆constraint,goto1);5) Computethepotential;

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6) Iftheswapdecreasesthepotential,accepttheswap.Iftheswapincreasesthepotential,acceptitwithprobability𝑒=∆R ,where∆𝑉isthechangeinpotentialduetotheswap;

7) Onlyiftheswapisaccepted,updatenurses’taskassignments,andpotential;8) Goto1).

VersionforW𝑆?3,𝑊𝑆=3:

1) Choosetwonurses(𝑖 ≠ 𝑗);2) Choosetwotimesteps(𝑡, 𝑠),sothat𝑖isactiveduring𝑡,andnotactiveduring𝑠,and𝑗is

activeduring𝑠,andnotactiveduring𝑡.Ifthisisnotpossible,goto1);3) Swaptasksbetween𝑖, 𝑗duringboth𝑡, 𝑠;4) Iftheswapbreaksthe𝑆constraint,goto1);5) Computethepotential;6) Iftheswapdecreasesthepotential,accepttheswap.Iftheswapincreasesthepotential,

acceptitwithprobability𝑒=∆R ,where∆𝑉isthechangeinpotentialduetotheswap;7) Onlyiftheswapisaccepted,updatenurses’taskassignments,andpotential;8) Goto1).

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